TL;DR
This paper investigates the conditions under which Killing vector fields exist in covariant metric theories, demonstrating that initial data symmetries are maintained during evolution in hyperbolic systems.
Contribution
It provides necessary and sufficient conditions for the existence of Killing vector fields in coupled gravity-matter systems and shows symmetry preservation during evolution.
Findings
Symmetries of initial data are preserved during evolution.
Conditions for existence of Killing vector fields are established.
Symmetry preservation applies to hyperbolic evolution systems.
Abstract
In covariant metric theories of coupled gravity-matter systems the necessary and sufficient conditions ensuring the existence of a Killing vector field are investigated. It is shown that the symmetries of initial data sets are preserved by the evolution of hyperbolic systems.
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